CPM Homework Help : CC3MN Problem 8-31

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8-31.

Simplify each exponential expression.

$2^4$
Hint (a):
$2 \left(2\right) \left(2\right) \left(2\right)$

$3^6$
Hint (b):
Multiply $3$ by itself $6$ times.
More Help (b):
$3 \left(3\right) \left(3\right) \left(3\right) \left(3\right) \left(3\right)$

$25^3$
Answer (c):
$15625$

$4^2$
Answer (d):
$16$

$9^3$
Hint (e):
$9 \left(9\right) \left(9\right)$
Answer (e):
$729$

$5^6$
Hint (f):
Multiply $5$ by itself $6$ times.

What patterns do you see between the expressions in parts (a) through (f) whose simplified forms are equal?

Hint (g):
(a) and (d), (b) and (e), (c) and (f) have the same answers. How is this possible?

Partial Answer (g):

Notice that the base in (d) is the square of the base in (a).
How does this apply to the other two pairs?

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